Let k be a field of characteristic p > 0. Call a finite group G a poco group over k if any finitely generated cohomological Mackey functor for G over k has polynomial growth. The main result of this paper is that G is a poco group over k if and only if the Sylow p-subgroups of G are cyclic, when p > 2, or have sectional rank at most 2, when p = 2. A major step in the proof is the case where G i...

We present a method to compute the geometric Picard rank of a K3 surface over Q. Contrary to a widely held belief, we show it is possible to verify Picard rank 1 using reduction only at a single prime. Our method is based on deformation theory for invertible sheaves.

This paper develops the spectral properties of pairwise comparison matrices (PCM) used in the multicriteria decision making method called analytic hierarchy process (AHP). Perturbed PCMs are introduced which may result in a reversal of the rank order of the decision alternatives. The analysis utilizes matrix theory to derive the principal eigenvector components of perturbed PCMs in explicit for...

With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set...

We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, and yet enables robust estimation in a broader variety of settings, including t...

Robustified rank tests, applying a robust scale estimator, are investigated for reliable and fast shift detection in time series. The tests show good power for sufficiently large shifts, low false detection rates for Gaussian noise and high robustness against outliers. Wilcoxon scores in combination with a robust and efficient scale estimator achieve good performance in many situations.

We give examples of non-isotrivial K3 surfaces over complex function fields with Zariski-dense rational points and NéronSeveri rank one.

The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong to the Martin boundary as well. In the case of the universal cover of a compact manifold with Ballmann rank one, we show that Martin points are generic and of...

SimRank is a well-known similarity measure between graph vertices. In this paper novel low-rank approximation of SimRank is proposed.

We classify joinings between a fairly general class of higher rank diagonalizable actions on locally homogeneous spaces. In particular, we classify joinings of the action of a maximal R-split torus on G/Γ, with G a simple Lie group of R-rank ≥ 2 and Γ < G a lattice. We deduce from this a classification of measurable factors of such actions, as well as certain equidistribution properties.